Systematic Presentation of Ritz Variational Method for the Flexural Analysis of Simply Supported Rectangular Kirchhoff–Love Plates

Ike, Charles Chinwuba

doi:10.21272/jes.2018.5(2).d1

Cited by 2 publications

(4 citation statements)

References 7 publications

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“…The basis functions F1n(x) and F2m(y) each satisfies the geometric and force equation at the supports for both bending and elastic buckling analysis. The GITM transforms the governing PDE for plate bending to the integral equation given by Equation (21) where the kernel function is expressed by Equation (22). The general solution of the integral equation is found for Cmn as Equation ( 25) which is expressible using integrals I1, I2, …, I8.…”

Section: Discussionmentioning

confidence: 99%

“…Ritz variational methodologies has been deployed for the formulation and solution of classical Kirchhoff plate problems by authors in [21][22][23].…”

Section: Theories Of Platesmentioning

confidence: 99%

“…In [21], the authors deployed Ritz technique for finding solutions to the bending analysis of rectangular Kirchhoff-Love plates subject to transverse hydrostatically varying loading distributions over the plate region. In [22], the author presented systematically the Ritz method for the flexural analysis of simply supported rectangular Kirchhoff plates under distributed transverse loadings. Similarly, in [23], the author used Ritz technique to solve the bending problems of rectangular thin plates resting on one parameter foundations, with the plate subject to uniformly distributed loading over the entire domain.…”

Section: Theories Of Platesmentioning

confidence: 99%

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Generalized Integral Transform Method for Bending and Buckling Analysis of Rectangular Thin Plate with Two Opposite Edges Simply Supported and Other Edges Clamped

Ike¹,

Onyia²,

Rowland-Lato³

2021

Adv. sci. technol. eng. syst. j.

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This paper presents the generalized integral transform method for solving flexural and elastic stability problems of rectangular thin plates clamped along /2 yb = and simply supported along remaining boundaries (x = 0, x = a) (CSCS plate). The considered plate is homogeneous, isotropic and carrying uniformly distributed transversely applied loading causing bending. Also studied, is a plate subject to (i) biaxial (ii) uniaxial uniform compressive load. The method uses the eigenfunctions of vibrating thin beams of equivalent span and support conditions in constructing the basis functions for the plate deflection and the integral kernel function. The transform is applied to the governing domain equation, converting the problem to integral equations for both cases of bending and elastic buckling. The integral equation reduces to algebraic problems for the bending problem, and algebraic eigenvalue problem for the elastic buckling problem. The deflections are obtained as double infinite series with rapidly convergent properties. Bending moments expressions are double series with infinite terms which are rapidly convergent. Maximum deflections and bending moments values occur at the plate centre in agreement with symmetry. The present results gave double series solutions with good convergent properties in closed form for bending problems. The resulting bending solutions were exact. Solving the resulting eigenvalue equation gave closed analytical equation for the buckling loads. Buckling loads are computed for the cases of biaxial and uniaxial uniform compression of square thin plates using one term approximations. The buckling load obtained for one term approximation of the eigenfunction gave results that are 12.23% greater than the exact solution. The use of more terms in the eigenfunction expansion could give more acceptable results for the eigenvalue problem of buckling of CSCS plates.

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Section: Discussionmentioning

confidence: 99%

“…Ritz variational methodologies has been deployed for the formulation and solution of classical Kirchhoff plate problems by authors in [21][22][23].…”

Section: Theories Of Platesmentioning

confidence: 99%

Section: Theories Of Platesmentioning

confidence: 99%

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Generalized Integral Transform Method for Bending and Buckling Analysis of Rectangular Thin Plate with Two Opposite Edges Simply Supported and Other Edges Clamped

Ike¹,

Onyia²,

Rowland-Lato³

2021

Adv. sci. technol. eng. syst. j.

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“…Ritz variational method has been used for plate problems by Ike [25], Ike [26] and Nwoji et al [27].…”

Section: Introductionmentioning

confidence: 99%

Single Finite Fourier Sine Integral Transform Method for the Flexural Analysis of Rectangular Kirchhoff Plate with Opposite Edges Simply Supported, Other Edges Clamped for the Case of Triangular Load Distribution

Mama¹,

Oguaghamba²,

Ike³

2020

International Journal of Engineering Research and Technology

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This paper presents the single finite Fourier sine integral transform method for the flexural analysis of rectangular Kirchhoff plate with opposite edges simply supported, and the other edges clamped for the case of triangular load distribution on the plate domain. The finite sine transform method is adopted because the sinusoidal integral kernel function satisfies all the Dirichlet boundary conditions along the simply supported edges. The governing domain equation which is a nonhomogeneous biharmonic equation is converted by the transformation to an integral equation over the solution domain. The integral equation is reduced by the linearity properties of the transformation, Leibnitz rule and boundary conditions along the simply supported edges to ordinary differential equations (ODEs). Classical methods of solving ODEs in closed-form were used to obtain the solutions that satisfy the boundary conditions along the clamped edges. Thus exact solutions to the boundary value problem that satisfy the governing equation at all points in the solution domain as well as at all points along the four edges are obtained. The resulting expression for the deflection is a single infinite series with demonstrated rapidly convergent properties. The bending moments Mxx, Myy expressions were obtained using the bending moment-deflection relations as infinite series with demonstrated rapid convergence. The converged values of the maximum deflection and bending moments Mxx, Myy evaluated at the plate centre are in excellent agreement with the previous exact results to the problem obtained by researchers who used the Kantorovich-Vlasov method; Levy's method; and the superposition method.

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Systematic Presentation of Ritz Variational Method for the Flexural Analysis of Simply Supported Rectangular Kirchhoff–Love Plates

Cited by 2 publications

References 7 publications

Generalized Integral Transform Method for Bending and Buckling Analysis of Rectangular Thin Plate with Two Opposite Edges Simply Supported and Other Edges Clamped

Generalized Integral Transform Method for Bending and Buckling Analysis of Rectangular Thin Plate with Two Opposite Edges Simply Supported and Other Edges Clamped

Single Finite Fourier Sine Integral Transform Method for the Flexural Analysis of Rectangular Kirchhoff Plate with Opposite Edges Simply Supported, Other Edges Clamped for the Case of Triangular Load Distribution

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